Question

A positive charge $'q'$ of mass $'m'$ is moving along the $+x$ axis. We wish to apply a uniform magnetic field $B$ for time $\Delta t$ so that the charge reverses its direction crossing the $y$ axis at a distance $d$. Then :

• A. $B=\frac{m\upsilon}{qd}$ and $\Delta\, t=\frac{\pi d}{\upsilon}$
• B. $B=\frac{m\upsilon }{2\:\,qd}\:$and$\:\Delta \:t=\frac{\pi \:d}{2\upsilon }$
• C. $B=\frac{2\,m\upsilon }{qd}\:$and$\:\Delta \:t=\frac{\pi \:d}{2\upsilon }$
• D. $B=\frac{2m\upsilon \:}{qd}\:$and$\:\Delta \:\:t=\frac{\pi \:\:d}{\upsilon \:}$

Answer 1

Answer: (C)

$R = \frac{d}{2}$
$\therefore Bqv=\frac{mv^{2}}{d/2}$
or, $B=\frac{2mv}{qd}$
Time interval for which a uniform magnetic field is applied
$\Delta t=\frac{\pi. \frac{d}{2}}{v}$
(particle reverses its direction after time At by covering semi circle).
$\Delta t=\frac{\pi d}{2v}$